wave_mechanics critical_thinking Question 23
Question: Consider ten identical sources of sound all giving the same frequency but having phase angles which are random. If the average intensity of each source is $ I _{0} $ , the average of resultant intensity I due to all these ten sources will be
[MP PMT 1990]
Options:
A) $ I=100I _{0} $
B) $ I=10I _{0} $
C) $ I=I _{0} $
D) $ I=\sqrt{10}I _{0} $
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Answer:
Correct Answer: B
Solution:
$\varphi $
In case of interference of two waves resultant intensity
$ I=I _{1}+I _{2}+2\sqrt{I _{1}I _{2}}\cos \varphi $
If f varies randomly with time, so $ \cos \varphi _{av}=0 $
Therefore $ I=I _{1}+I _{2} $
For n identical waves, $ I=I _{0}+I _{0}+…….=nI _{0} $ here $ I=10I _{0}.
$
BETA
